Struct rug::rational::SmallRational [] [src]

#[repr(C)]
pub struct SmallRational { /* fields omitted */ }

A small rational number that does not require any memory allocation.

This can be useful when you have a numerator and denominator that are 32-bit or 64-bit integers and you need a reference to a Rational.

Although no allocation is required, setting the value of a SmallRational does require some computation, as the numerator and denominator need to be canonicalized.

The SmallRational type can be coerced to a Rational, as it implements Deref with a Rational target.

Examples

use rug::Rational;
use rug::rational::SmallRational;
// `a` requires a heap allocation
let mut a = Rational::from((100, 13));
// `b` can reside on the stack
let b = SmallRational::from((-100, 21));
a /= &*b;
assert_eq!(*a.numer(), -21);
assert_eq!(*a.denom(), 13);

Methods

impl SmallRational
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Creates a SmallRational with value 0.

Examples

use rug::rational::SmallRational;
let r = SmallRational::new();
// Use r as if it were Rational.
assert_eq!(*r.numer(), 0);
assert_eq!(*r.denom(), 1);

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Creates a SmallRational from a 32-bit numerator and denominator, assuming they are in canonical form.

Safety

This function is unsafe because

  • it does not check that the denominator is not zero, and

  • it does not canonicalize the numerator and denominator.

The rest of the library assumes that SmallRational and Rational structures keep their numerators and denominators canonicalized.

Examples

use rug::rational::SmallRational;
let from_unsafe = unsafe {
    SmallRational::from_canonicalized_32(true, 13, 10)
};
// from_safe is canonicalized to the same form as from_unsafe
let from_safe = SmallRational::from((130, -100));
assert_eq!(from_unsafe.numer(), from_safe.numer());
assert_eq!(from_unsafe.denom(), from_safe.denom());

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Creates a SmallRational from a 64-bit numerator and denominator, assuming they are in canonical form.

Safety

This function is unsafe because

  • it does not check that the denominator is not zero, and

  • it does not canonicalize the numerator and denominator.

The rest of the library assumes that SmallRational and Rational structures keep their numerators and denominators canonicalized.

Examples

use rug::rational::SmallRational;
let from_unsafe = unsafe {
    SmallRational::from_canonicalized_64(true, 13, 10)
};
// from_safe is canonicalized to the same form as from_unsafe

let from_safe = SmallRational::from((130, -100));
assert_eq!(from_unsafe.numer(), from_safe.numer());
assert_eq!(from_unsafe.denom(), from_safe.denom());

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Sets a SmallRational to a 32-bit numerator and denominator, assuming they are in canonical form.

Safety

This function is unsafe because

  • it does not check that the denominator is not zero, and

  • it does not canonicalize the numerator and denominator.

The rest of the library assumes that SmallRational and Rational structures keep their numerators and denominators canonicalized.

Examples

use rug::rational::SmallRational;
let mut from_unsafe = SmallRational::new();
unsafe {
    from_unsafe.assign_canonicalized_32(true, 13, 10)
};
// from_safe is canonicalized to the same form as from_unsafe
let from_safe = SmallRational::from((130, -100));
assert_eq!(from_unsafe.numer(), from_safe.numer());
assert_eq!(from_unsafe.denom(), from_safe.denom());

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Sets a SmallRational to a 64-bit numerator and denominator, assuming they are in canonical form.

Safety

This function is unsafe because

  • it does not check that the denominator is not zero, and

  • it does not canonicalize the numerator and denominator.

The rest of the library assumes that SmallRational and Rational structures keep their numerators and denominators canonicalized.

Examples

use rug::rational::SmallRational;
let mut from_unsafe = SmallRational::new();
unsafe {
    from_unsafe.assign_canonicalized_64(true, 13, 10)
};
// from_safe is canonicalized to the same form as from_unsafe
let from_safe = SmallRational::from((130, -100));
assert_eq!(from_unsafe.numer(), from_safe.numer());
assert_eq!(from_unsafe.denom(), from_safe.denom());

Methods from Deref<Target = Rational>

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Converts to an Integer, rounding towards zero.

Examples

use rug::Rational;
let pos = Rational::from((139, 10));
let posi = pos.to_integer();
assert_eq!(posi, 13);
let neg = Rational::from((-139, 10));
let negi = neg.to_integer();
assert_eq!(negi, -13);

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Converts to an Integer inside i, rounding towards zero.

Examples

use rug::{Integer, Rational};
let mut i = Integer::new();
assert_eq!(i, 0);
let pos = Rational::from((139, 10));
pos.copy_to_integer(&mut i);
assert_eq!(i, 13);
let neg = Rational::from((-139, 10));
neg.copy_to_integer(&mut i);
assert_eq!(i, -13);

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Converts to an f32, rounding towards zero.

Examples

use rug::Rational;
use rug::rational::SmallRational;
use std::f32;
let min = Rational::from_f32(f32::MIN).unwrap();
let minus_small = min - &*SmallRational::from((7, 2));
// minus_small is truncated to f32::MIN
assert_eq!(minus_small.to_f32(), f32::MIN);
let times_three_two = minus_small * &*SmallRational::from((3, 2));
// times_three_two is too small
assert_eq!(times_three_two.to_f32(), f32::NEG_INFINITY);

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Converts to an f64, rounding towards zero.

Examples

use rug::Rational;
use rug::rational::SmallRational;
use std::f64;

// An `f64` has 53 bits of precision.
let exact = 0x1f_1234_5678_9aff_u64;
let den = 0x1000_u64;
let r = Rational::from((exact, den));
assert_eq!(r.to_f64(), exact as f64 / den as f64);

// large has 56 ones
let large = 0xff_1234_5678_9aff_u64;
// trunc has 53 ones followed by 3 zeros
let trunc = 0xff_1234_5678_9af8_u64;
let j = Rational::from((large, den));
assert_eq!(j.to_f64(), trunc as f64 / den as f64);

let max = Rational::from_f64(f64::MAX).unwrap();
let plus_small = max + &*SmallRational::from((7, 2));
// plus_small is truncated to f64::MAX
assert_eq!(plus_small.to_f64(), f64::MAX);
let times_three_two = plus_small * &*SmallRational::from((3, 2));
// times_three_two is too large
assert_eq!(times_three_two.to_f64(), f64::INFINITY);

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Returns a string representation for the specified radix.

Examples

use rug::Rational;
let r1 = Rational::from(0);
assert_eq!(r1.to_string_radix(10), "0");
let r2 = Rational::from((15, 5));
assert_eq!(r2.to_string_radix(10), "3");
let r3 = Rational::from((10, -6));
assert_eq!(r3.to_string_radix(10), "-5/3");
assert_eq!(r3.to_string_radix(5), "-10/3");

Panics

Panics if radix is less than 2 or greater than 36.

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Borrows the numerator as an Integer.

Examples

use rug::Rational;
let r = Rational::from((12, -20));
// r will be canonicalized to -3 / 5
assert_eq!(*r.numer(), -3)

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Borrows the denominator as an Integer.

Examples

use rug::Rational;
let r = Rational::from((12, -20));
// r will be canonicalized to -3 / 5
assert_eq!(*r.denom(), 5);

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Borrows the numerator and denominator as Integer values.

Examples

use rug::Rational;
let r = Rational::from((12, -20));
// r will be canonicalized to -3 / 5
let (num, den) = r.as_numer_denom();
assert_eq!(*num, -3);
assert_eq!(*den, 5);

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Converts into numerator and denominator integers.

This function reuses the allocated memory and does not allocate any new memory.

Examples

use rug::Rational;
let r = Rational::from((12, -20));
// r will be canonicalized to -3 / 5
let (num, den) = r.into_numer_denom();
assert_eq!(num, -3);
assert_eq!(den, 5);

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Borrows a negated copy of the Rational number.

The returned object implements Deref with a Rational target. This method performs a shallow copy and negates it, and negation does not change the allocated data.

Examples

use rug::Rational;
let r = Rational::from((7, 11));
let neg_r = r.as_neg();
assert_eq!(*neg_r, (-7, 11));
// methods taking &self can be used on the returned object
let reneg_r = neg_r.as_neg();
assert_eq!(*reneg_r, (7, 11));
assert_eq!(*reneg_r, r);

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Borrows an absolute copy of the Rational number.

The returned object implements Deref with a Rational target. This method performs a shallow copy and possibly negates it, and negation does not change the allocated data.

Examples

use rug::Rational;
let r = Rational::from((-7, 11));
let abs_r = r.as_abs();
assert_eq!(*abs_r, (7, 11));
// methods taking &self can be used on the returned object
let reabs_r = abs_r.as_abs();
assert_eq!(*reabs_r, (7, 11));
assert_eq!(*reabs_r, *abs_r);

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Borrows a reciprocal copy of the Rational number.

The returned object implements Deref with a Rational target. This method performs some shallow copying, swapping numerator and denominator and making sure the sign is in the numerator.

Examples

use rug::Rational;
let r = Rational::from((-7, 11));
let recip_r = r.as_recip();
assert_eq!(*recip_r, (-11, 7));
// methods taking &self can be used on the returned object
let rerecip_r = recip_r.as_recip();
assert_eq!(*rerecip_r, (-7, 11));
assert_eq!(*rerecip_r, r);

Panics

Panics if the value is zero.

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Returns the same result as self.cmp(&0), but is faster.

Examples

use rug::Rational;
use std::cmp::Ordering;
assert_eq!(Rational::from((-5, 7)).cmp0(), Ordering::Less);
assert_eq!(Rational::from(0).cmp0(), Ordering::Equal);
assert_eq!(Rational::from((5, 7)).cmp0(), Ordering::Greater);

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Computes the absolute value.

Examples

use rug::Rational;
let r = Rational::from((-100, 17));
let abs = r.abs();
assert_eq!(abs, (100, 17));

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Computes the absolute value.

Examples

use rug::Rational;
let r = Rational::from((-100, 17));
let r_ref = r.abs_ref();
let abs = Rational::from(r_ref);
assert_eq!(abs, (100, 17));

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Clamps the value within the specified bounds.

Examples

use rug::Rational;
let min = (-3, 2);
let max = (3, 2);
let too_small = Rational::from((-5, 2));
let clamped1 = too_small.clamp(&min, &max);
assert_eq!(clamped1, (-3, 2));
let in_range = Rational::from((1, 2));
let clamped2 = in_range.clamp(&min, &max);
assert_eq!(clamped2, (1, 2));

Panics

Panics if the maximum value is less than the minimum value.

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Clamps the value within the specified bounds.

Examples

use rug::Rational;
let min = (-3, 2);
let max = (3, 2);
let too_small = Rational::from((-5, 2));
let r1 = too_small.clamp_ref(&min, &max);
let clamped1 = Rational::from(r1);
assert_eq!(clamped1, (-3, 2));
let in_range = Rational::from((1, 2));
let r2 = in_range.clamp_ref(&min, &max);
let clamped2 = Rational::from(r2);
assert_eq!(clamped2, (1, 2));

Panics

Panics if the maximum value is less than the minimum value.

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Computes the reciprocal.

Examples

use rug::Rational;
let r = Rational::from((-100, 17));
let recip = r.recip();
assert_eq!(recip, (-17, 100));

Panics

Panics if the value is zero.

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Computes the reciprocal.

Examples

use rug::Rational;
let r = Rational::from((-100, 17));
let r_ref = r.recip_ref();
let recip = Rational::from(r_ref);
assert_eq!(recip, (-17, 100));

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Rounds the number towards zero and returns it as an Integer.

Examples

use rug::Rational;
// -3.7
let r1 = Rational::from((-37, 10));
let i1 = r1.trunc();
assert_eq!(i1, -3);
// 3.3
let r2 = Rational::from((33, 10));
let i2 = r2.trunc();
assert_eq!(i2, 3);

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Rounds the number towards zero.

Examples

use rug::{Assign, Integer, Rational};
let mut trunc = Integer::new();
// -3.7
let r1 = Rational::from((-37, 10));
trunc.assign(r1.trunc_ref());
assert_eq!(trunc, -3);
// 3.3
let r2 = Rational::from((33, 10));
trunc.assign(r2.trunc_ref());
assert_eq!(trunc, 3);

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Deprecated since 0.9.0

: renamed to rem_trunc

Computes the fractional part of the number.

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Deprecated since 0.9.0

: renamed to rem_trunc_ref

Computes the fractional part of the number.

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Computes the fractional part of the number.

Examples

use rug::Rational;
// -100/17 = -5 - 15/17
let r = Rational::from((-100, 17));
let rem = r.rem_trunc();
assert_eq!(rem, (-15, 17));

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Computes the fractional part of the number.

Examples

use rug::Rational;
// -100/17 = -5 - 15/17
let r = Rational::from((-100, 17));
let r_ref = r.rem_trunc_ref();
let rem = Rational::from(r_ref);
assert_eq!(rem, (-15, 17));

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Computes the fractional and truncated parts of the number.

The initial value of trunc is ignored.

Examples

use rug::{Integer, Rational};
// -100/17 = -5 - 15/17
let r = Rational::from((-100, 17));
let (fract, trunc) = r.fract_trunc(Integer::new());
assert_eq!(fract, (-15, 17));
assert_eq!(trunc, -5);

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Computes the fractional and truncated parts of the number.

Examples

use rug::{Assign, Integer, Rational};
// -100/17 = -5 - 15/17
let r = Rational::from((-100, 17));
let r_ref = r.fract_trunc_ref();
let (mut fract, mut trunc) = (Rational::new(), Integer::new());
(&mut fract, &mut trunc).assign(r_ref);
assert_eq!(fract, (-15, 17));
assert_eq!(trunc, -5);

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Rounds the number upwards (towards plus infinity) and returns it as an Integer.

Examples

use rug::Rational;
// -3.7
let r1 = Rational::from((-37, 10));
let i1 = r1.ceil();
assert_eq!(i1, -3);
// 3.3
let r2 = Rational::from((33, 10));
let i2 = r2.ceil();
assert_eq!(i2, 4);

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Rounds the number upwards (towards plus infinity).

Examples

use rug::{Assign, Integer, Rational};
let mut ceil = Integer::new();
// -3.7
let r1 = Rational::from((-37, 10));
ceil.assign(r1.ceil_ref());
assert_eq!(ceil, -3);
// 3.3
let r2 = Rational::from((33, 10));
ceil.assign(r2.ceil_ref());
assert_eq!(ceil, 4);

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Computes the non-positive remainder after rounding up.

Examples

use rug::Rational;
// 100/17 = 6 - 2/17
let r = Rational::from((100, 17));
let rem = r.rem_ceil();
assert_eq!(rem, (-2, 17));

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Computes the non-positive remainder after rounding up.

Examples

use rug::Rational;
// 100/17 = 6 - 2/17
let r = Rational::from((100, 17));
let r_ref = r.rem_ceil_ref();
let rem = Rational::from(r_ref);
assert_eq!(rem, (-2, 17));

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Computes the fractional and ceil parts of the number.

The fractional part cannot greater than zero. The initial value of ceil is ignored.

Examples

use rug::{Integer, Rational};
// 100/17 = 6 - 2/17
let r = Rational::from((100, 17));
let (fract, ceil) = r.fract_ceil(Integer::new());
assert_eq!(fract, (-2, 17));
assert_eq!(ceil, 6);

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Computes the fractional and ceil parts of the number.

The fractional part cannot be greater than zero.

Examples

use rug::{Assign, Integer, Rational};
// 100/17 = 6 - 2/17
let r = Rational::from((100, 17));
let r_ref = r.fract_ceil_ref();
let (mut fract, mut ceil) = (Rational::new(), Integer::new());
(&mut fract, &mut ceil).assign(r_ref);
assert_eq!(fract, (-2, 17));
assert_eq!(ceil, 6);

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Rounds the number downwards (towards minus infinity) and returns it as an Integer.

Examples

use rug::Rational;
// -3.7
let r1 = Rational::from((-37, 10));
let i1 = r1.floor();
assert_eq!(i1, -4);
// 3.3
let r2 = Rational::from((33, 10));
let i2 = r2.floor();
assert_eq!(i2, 3);

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Rounds the number downwards (towards minus infinity).

Examples

use rug::{Assign, Integer, Rational};
let mut floor = Integer::new();
// -3.7
let r1 = Rational::from((-37, 10));
floor.assign(r1.floor_ref());
assert_eq!(floor, -4);
// 3.3
let r2 = Rational::from((33, 10));
floor.assign(r2.floor_ref());
assert_eq!(floor, 3);

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Computes the non-negative remainder after rounding down.

Examples

use rug::Rational;
// -100/17 = -6 + 2/17
let r = Rational::from((-100, 17));
let rem = r.rem_floor();
assert_eq!(rem, (2, 17));

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Computes the non-negative remainder after rounding down.

Examples

use rug::Rational;
// -100/17 = -6 + 2/17
let r = Rational::from((-100, 17));
let r_ref = r.rem_floor_ref();
let rem = Rational::from(r_ref);
assert_eq!(rem, (2, 17));

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Computes the fractional and floor parts of the number.

The fractional part cannot be negative. The initial value of floor is ignored.

Examples

use rug::{Integer, Rational};
// -100/17 = -6 + 2/17
let r = Rational::from((-100, 17));
let (fract, floor) = r.fract_floor(Integer::new());
assert_eq!(fract, (2, 17));
assert_eq!(floor, -6);

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Computes the fractional and floor parts of the number.

The fractional part cannot be negative.

Examples

use rug::{Assign, Integer, Rational};
// -100/17 = -6 + 2/17
let r = Rational::from((-100, 17));
let r_ref = r.fract_floor_ref();
let (mut fract, mut floor) = (Rational::new(), Integer::new());
(&mut fract, &mut floor).assign(r_ref);
assert_eq!(fract, (2, 17));
assert_eq!(floor, -6);

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Rounds the number to the nearest integer and returns it as an Integer.

When the number lies exactly between two integers, it is rounded away from zero.

Examples

use rug::Rational;
// -3.5
let r1 = Rational::from((-35, 10));
let i1 = r1.round();
assert_eq!(i1, -4);
// 3.7
let r2 = Rational::from((37, 10));
let i2 = r2.round();
assert_eq!(i2, 4);

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Rounds the number to the nearest integer.

When the number lies exactly between two integers, it is rounded away from zero.

Examples

use rug::{Assign, Integer, Rational};
let mut round = Integer::new();
// -3.5
let r1 = Rational::from((-35, 10));
round.assign(r1.round_ref());
assert_eq!(round, -4);
// 3.7
let r2 = Rational::from((37, 10));
round.assign(r2.round_ref());
assert_eq!(round, 4);

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Computes the remainder after rounding to the nearest integer.

Examples

use rug::Rational;
// -3.5 = -4 + 0.5 = -4 + 1/2
let r1 = Rational::from((-35, 10));
let rem1 = r1.rem_round();
assert_eq!(rem1, (1, 2));
// 3.7 = 4 - 0.3 = 4 - 3/10
let r2 = Rational::from((37, 10));
let rem2 = r2.rem_round();
assert_eq!(rem2, (-3, 10));

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Computes the remainder after rounding to the nearest integer.

Examples

use rug::Rational;
// -3.5 = -4 + 0.5 = -4 + 1/2
let r1 = Rational::from((-35, 10));
let r_ref1 = r1.rem_round_ref();
let rem1 = Rational::from(r_ref1);
assert_eq!(rem1, (1, 2));
// 3.7 = 4 - 0.3 = 4 - 3/10
let r2 = Rational::from((37, 10));
let r_ref2 = r2.rem_round_ref();
let rem2 = Rational::from(r_ref2);
assert_eq!(rem2, (-3, 10));

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Computes the fractional and rounded parts of the number.

The fractional part is positive when the number is rounded down and negative when the number is rounded up. When the number lies exactly between two integers, it is rounded away from zero.

Examples

use rug::{Integer, Rational};
// -3.5 = -4 + 0.5 = -4 + 1/2
let r1 = Rational::from((-35, 10));
let (fract1, round1) = r1.fract_round(Integer::new());
assert_eq!(fract1, (1, 2));
assert_eq!(round1, -4);
// 3.7 = 4 - 0.3 = 4 - 3/10
let r2 = Rational::from((37, 10));
let (fract2, round2) = r2.fract_round(Integer::new());
assert_eq!(fract2, (-3, 10));
assert_eq!(round2, 4);

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Computes the fractional and round parts of the number.

The fractional part is positive when the number is rounded down and negative when the number is rounded up. When the number lies exactly between two integers, it is rounded away from zero.

Examples

use rug::{Assign, Integer, Rational};
// -3.5 = -4 + 0.5 = -4 + 1/2
let r1 = Rational::from((-35, 10));
let r_ref1 = r1.fract_round_ref();
let (mut fract1, mut round1) = (Rational::new(), Integer::new());
(&mut fract1, &mut round1).assign(r_ref1);
assert_eq!(fract1, (1, 2));
assert_eq!(round1, -4);
// 3.7 = 4 - 0.3 = 4 - 3/10
let r2 = Rational::from((37, 10));
let r_ref2 = r2.fract_round_ref();
let (mut fract2, mut round2) = (Rational::new(), Integer::new());
(&mut fract2, &mut round2).assign(r_ref2);
assert_eq!(fract2, (-3, 10));
assert_eq!(round2, 4);

Trait Implementations

impl Default for SmallRational
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Returns the "default value" for a type. Read more

impl Deref for SmallRational
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The resulting type after dereferencing.

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Dereferences the value.

impl<T> From<T> for SmallRational where
    SmallRational: Assign<T>, 
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Performs the conversion.

impl Assign<i32> for SmallRational
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Peforms the assignement. Read more

impl Assign<i64> for SmallRational
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Peforms the assignement. Read more

impl Assign<u32> for SmallRational
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Peforms the assignement. Read more

impl Assign<u64> for SmallRational
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Peforms the assignement. Read more

impl Assign<(i32, i32)> for SmallRational
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Peforms the assignement. Read more

impl Assign<(i64, i64)> for SmallRational
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Peforms the assignement. Read more

impl Assign<(i32, u32)> for SmallRational
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Peforms the assignement. Read more

impl Assign<(i64, u64)> for SmallRational
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Peforms the assignement. Read more

impl Assign<(u32, i32)> for SmallRational
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Peforms the assignement. Read more

impl Assign<(u64, i64)> for SmallRational
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Peforms the assignement. Read more

impl Assign<(u32, u32)> for SmallRational
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Peforms the assignement. Read more

impl Assign<(u64, u64)> for SmallRational
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Peforms the assignement. Read more